SUSY Models

Standard Model (SM) – 18 (+xν) free parameters

Minimal Super Symmetry Model (MSSM) – 105 (+45) additional free parameters

First important choice: mechanism of symmetry breakingAssume “hidden sector” – neutral w.r.t. SM gauge groups

SUSY breaking occurs in the hidden sector;It is transmitted to visible MSSM particles by some “messenger particles”• Gravity Mediated Supersymmetry Breaking (mSUGRA)

• Gauge Mediated Supersymmetry Breaking (GMSB)

• Anomaly Mediated Supersymmetry Breaking (AMSB), . . .

For phenomenology: make some “reasonable assumptions” and use ∼5–6 parameters only.

mSUGRA

SUSY is broken by gravity

Assume universal masses at GUT scale:m0 – common mass of scalars (squarks, sleptons, Higgs bosons)m1/2 – common mass of gauginos and higgsinosA0 – common trilinear couplingtanβ – ratio of Higgs vacuum expectation valuessignµ = ±1 – sign of µ SUSY conserving Higgsino mass parameter

Typical mSUGRA Spectrum

0

200

400

600

800

qL~~

~

~

q

τ

τ

R

2

1

~g

~� 04 ;

~�

+2

~� 03

~� 02 ;

~�

+1

~� 01

~

~

l

l

L

R

;

;h

H,AH+

~t1

Point SU3

M (

GeV

)

J = 0 J = 1/2

~b1

χ

χ χ

χχχ

R-Parity

MSSM allows a rapid proton decay: p→ e+π0

Current experimental limit: τp > 1.6 · 1033 years.

Solution: conservation of R-Parity (Matter Parity):

R= (−1)2S+3B+L S – spin, B – baryon number, L – lepton number

For all SM particles: R= 1 For all superpartners: R= −1

Consequences:• Eliminates 45 free parameters (105 remain)• Baryon and lepton numbers are very well conserved• Superpartners are always produced in pairs• The lightest supersymmetric partner (LSP) is stable

LSPs can be dark matter! Should be neutral and not strongly interacting=⇒ Neutralino

Grand Unification Theory (GUT)

10log Q / eV

1/α i

1/α1

1/α2

1/α3

MSSM

10log Q / eV

1/α i

0

10

20

30

40

50

60

0 5 10 150

10

20

30

40

50

60

0 5 10 15

◮◮ SUSY can help gauge coupling unification!

SUSY Production at LHC

• In most cases new particles are short-lived.We don’t “see” them directly in detectorbut reconstruct from hadron jets, leptons, photons

• Everything is produced at once in long decay chains.Dominant backgrounds are combinatorial from SUSY itself.=⇒ Cannot study the production of one sparticle in isolation.=⇒ Must use a consistent model for simulation.

q

q

q

q

q~

~

~

~

—

—

—b

b

l+

l+

g

~g

W—W+t

t

t1

ν

χ1

~χ10

~χ20

3 isolated leptons+ 2 b-jets+ 4 jets+ Et,miss

~l

+

l-

Missing ET

• 2 LSPs at the end of decay chains =⇒ missing energy

• Parton-parton interactions: p1 = x1P, p2 = x2P=⇒ centre-of-mass is always boostedNo information from longitudinal momentum component

=⇒⇐=

• Missing transverse momentum is the signature

• Masses are neglected =⇒ missing “transverse energy” ET

Simulation: SUSY Event in ATLAS

SUSY Signatures at the LHC

Decay cascades down to LSPs. Features:

• Large Missing ET

• High ET jets

• Many b quarks

• Many isolated leptons

q

q

q

q

q~

~

~

~

—

—

—b

b

l+

l+

g

~g

W—W+t

t

t1

ν

χ1

~χ10

~χ20

3 isolated leptons+ 2 b-jets+ 4 jets+ Et,miss

~l

+

l-

Discovery is “easy” in inclusive measurements

Discovery Potential – Example mSUGRA

• Select ≥ 4 jets and ET,miss

• Reconstruct effective mass

Meff =4

∑

i=1

|PT,i | + |ET,miss |

LHC Point 5

10-13

10-12

10-11

10-10

10-9

10-8

10-7

0 1000 2000 3000 4000Meff (GeV)

dσ/d

Mef

f (m

b/40

0 G

eV)

At high Meff SUSY rises above SM

• Inclusive signatures provide evidence

up to 2.5 TeV for squarks and gluinos

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

0 500 1000 1500 2000

m0 (GeV)

m1/

2(G

eV)

mSUGRA reach in ETmiss

+ jets final state

1 month, low lumi (1 fb −1)

1 year, low lumi (10 fb −1)

1 year, high lumi (100 fb −1)

3 years, high lumi (300 fb −1)

g~(500)

g~(1000)

g~(1500)

g~(2000)

g~(2500)

g~(3000)

q ~(2500)

q~(2000)

q ~(1500)q ~(1000)

q~(500)

h (114) mass limit

h(123)

A0 = 0 , tanβ = 35 , µ > 0

Cha

rged

LSP

Chargino Searches at LEP

No symmetry breaking

• Energy of LHC is most crucial.Reach increases slowly with luminosity.

Discovery Potential – Adding Leptons

• Monte Carlo may underestimate SMbackgrounds from multi-jet final states

(Problems: NLO ME+PS . . . )

• Select ≥ 2 jets + ET,miss + 0l (l veto),1l, 2l opposite sign, 2l same sign, 3l

• Cumulative reach can be even better

than inclusive

Accessible SUSY mass range:0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

0 500 1000 1500 2000

m0 (GeV)

m1/

2(G

eV)

mSUGRA reach in various final states for 100 fb−1

ETmiss

0l

0l + 1l + 2l OS

1l

2l OS2l SS

3l

g~(500)

g~(1000)

g~(1500)

g~(2000)

g~(2500)

g~(3000)

q ~(2500)

q~(2000)

q~(1500)q~(1000)

q~(500)

h (114) mass limit

h(123)

A0 = 0 , tanβ = 35 , µ > 0

Cha

rged

LSP

Chargino Searches at LEP

No symmetry breaking

Collider Weakly coupled Strongly coupled

LEP 100 GeV 100 GeV

Tevatron 100 GeV 300 GeV

LHC 500 GeV 2500 GeV

SUSY Particle Mass Reconstruction

Using edges, thresholds and endpoints in invariant mass distributions

Example GMSB: LSP is gravitino G̃ with mG̃ ∼ eV− keV.Different GMSB models depending on Next-to-Lightest Supersymmetric Particle (NLSP)Consider here NLSP to be short-lived neutralino χ̃01

χ̃02 → l̃± l∓

x→ χ̃01 l±

x→ G̃γ

chain of three 2-body decays

mχ̃02 ,mχ̃01 ,ml̃ unknown, mG̃ neglected

2 χ̃01 in event. Selection:

• 2 hard isolated photons make SM background negligible

• At least 2 leptons

• Missing ET from gravitinos and possibly neutrinos

• Large Meff (possibly jets . . . )

SUSY Particle Mass Reconstruction

Using edges, thresholds and endpoints in invariant mass distributions

• Plot e+e− + µ+µ− − e±µ∓ to subtract SUSY and small SM background

• Select γ with the smaller Mllγ

0

50

100

150

0 50 100 150 200 250Mllγ (GeV)

ee+

µµ-e

µ E

vent

s/2.

5 G

eV/1

0 fb

-1

Mmaxllγ

Mmaxllγ =√

m2χ̃02−m2

χ̃01with 0.2− 0.5 GeVprecision

SUSY Particle Mass Reconstruction

Using edges, thresholds and endpoints in invariant mass distributions

0

50

100

150

200

0 50 100 150 200 250Mll (GeV)

ee+

µµ-e

µ E

vent

s/2.

5 G

eV/1

0 fb

-1 Mmaxll

Mmaxll = mχ̃02

√

√

√

√

1−m2

l̃R

m2χ̃02

√

√

√

√

1−m2χ̃01

m2l̃R

0

50

100

150

0 50 100 150 200 250Mlγ (GeV)

ee+

µµ-e

µ E

vent

s/2.

5 G

eV/1

0 fb

-1

M(1)lγ

M(2)lγ

M(1)lγ =√

m2l̃R−m2

χ̃01− “adjacent” lγ pair

M(2)lγ =√

m2χ̃02−m2

l̃R− “further” lγ pair

◮◮ mχ̃02 ,mχ̃01 ,ml̃ are found from Mmaxll , M

(1)lγ , M

(2)lγ

(Quasi-)Stable Coloured Hadrons: R-Hadrons

• LSP is gluino (in Split-SUSY)• Long-lived squark (t̃ in GMSB or SUSY-5D)

hadronise into heavy (mR & 100 GeV) bound states: R-hadrons (g̃g, g̃qq̄, g̃qqq, q̃q̄, q̃qq)

Heavy almost non-interacting core surrounded by cloud of light quarks• “Cannon ball”

• Low energy particles are produced on the way• Exchanges charge e.g. R+ + n→ R− + p+ π+

PYTHIA R-hadron Event from ATLSIM

R-hadron

Interactions of R-hadrongiving off low energy pions

R-hadron

(Quasi-)Stable Coloured Hadrons: R-Hadrons

• LSP is gluino (in Split-SUSY)• Long-lived squark (t̃ in GMSB or SUSY-5D)

hadronise into heavy (mR & 100 GeV) bound states: R-hadrons (g̃g, g̃qq̄, g̃qqq, q̃q̄, q̃qq)

Heavy almost non-interacting core surrounded by cloud of light quarks• “Cannon ball”

• Low energy particles are produced on the way• Exchanges charge e.g. R+ + n→ R− + p+ π+

Signatures• Large ionisation in tracker (Bethe-Bloch)

• Time-of-Flight in µ systems• Specific E/p – calo energy / track momentum

• Specific shower shapes• Charge flips between tracker and µ-system

can be used to find particle type0

10

20

30

40

50

60

70

80

90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Emeasured/pmeasured

Nr

of

even

ts

Muon

R-hadron M=300 GeV/c2

R-hadron M=20 GeV/c2

Pion

P=100 GeV/c

Arguments for SUSY

• Rich, calculable, self-consistent beyond-the-SM theory• “Obvious” symmetry extension

• Gauge coupling unification• Can solve gauge hierarchy problem

• Source of dark matter (R-parity)• String theory seems to like it

Challenges for Low Energy SUSY

“Throw a dart into Minimal SUSY parameter space,And what do you get?

Observable predictions would be incompatible with experiment.”

• Proton decay (at higher orders also with conserved R-parity)• Flavor Changing Neutral Currents• Many new sources for CP Violation• Full calculation of Higgs mass=⇒ Suggest high masses for scalars: Several TeV− PeV

• Gauge coupling unification• Cold dark matter=⇒ . . . -inos are lighter: ∼ 100 GeV− 2.5 TeV

“Naturalness” strained?

Scenarios for SUSY at the LHC

DPessimistic scenarios:• SUSY does not exist.• SUSY can be out of reach (if MLSP & 2 TeV).

• SUSY can be there but only in very challenging signatures.UOptimistic scenarios:• SUSY will be found and clearly recognised.

• Something looking like SUSY will be found.International Linear e+e− Collider (ILC) will give the final answer.

Compactified Extra Dimensions

Planck scale can be just around the corner ∼ 1TeV⇒ No need to go far away in energy with SM

This can be accomplished by means of Extra Dimensions

First considered by Nordström (1914), Kaluza (1921) and Klein (1926)to unify gravity and e.m. force. Later revival in string theory

Large Extra Dimensions

ADD approach Antoniadis, Arkani-Hamed, Dimopoulos, Dvali: hep-ph/9803315, 9804398, 9807344There are n compactified extra dimensionsOnly gravity can propagate in extra dimensions

Using Gauss law

F ∝Gr2−→ F ∝

G′

r2+n

For r ≫ RC: F ∝G′

r2RnC

For a smooth transition

G′ ∼ GRnC

New Fundamental Planck Scale

“Visible” 4-dim. Planck scale

MPl =

√

~cG

⇐⇒ G =~c

M2Pl

“Real” D-dim. Planck scale (D = 4+ n)where gravity gets strong

MD ∝n+2

√

~cG′

⇐⇒ G′ =~c

M2+nD

From that follows

G′ ∼ GRnC ⇐⇒ M2Pl ∼ M

n+2D R

nC

Size of extra dimension

RC ∼1

MD

(

MPlMD

)2n

.

−→ Large RC ⇐⇒ Small MD

http://xxx.lanl.gov/abs/hep-ph/9803315http://xxx.lanl.gov/abs/hep-ph/9804398http://xxx.lanl.gov/abs/hep-ph/9807344

Possible Sizes of Extra Dimensions

Set MD = 1 TeV to solve the hierarchy problem.No need for fine tuning any more!

Size for MD = 1 TeV :

n 1 2 3 . . . 7

RC 1010 km 1 mm 1 nm . . . 1 fm↑ ↑ ↑ ↑

O(Solar system) “large”

compared to HEP scales

SM gauge fields cannot go to extra dimensions at such scales.This is ruled out by HEP experiments. But gravity can!

At present, Newton’s gravity law is tested down to ∼50 µm [hep-ph/0611184]

Motivation by the String Theory

• String theory

3d−brane

the brainconfined toopen strings

closed stringsare free

SM gauge fields gravity

String theories require 6 or 7 extra dimensions, but not necessary of the same size

• Why gravity? Because it couples to energy/momentum.If gravity cannot go to extra dimensions, then also no other force can.

http://xxx.lanl.gov/abs/hep-ph/0611184

Kaluza–Klein Gravitons in ADD

• Winding modes

• Energy spacing ∼ 1/RC ∼ 1 meV− 100 MeV (large ED)

Appear as continuous spectrum in experimentMass: m2 = E2 −

∑Di=1 p

2i = 0.

Effective mass: m2 = E2 −∑3

i=1 p2i

• Search for production of

–– real gravitons → monojets, monophotons

–– virtual gravitons → e+e−, µ+µ−, γγ

Monojets

Real graviton production

p

p

qjet

G

Signal: high ET jet + missing ET

Monojets – Standard Model Backgrounds

• Jet + Z→ νν̄• Jet + W→ νe, νµ, ντ with lepton lost

(lepton with low energy, lepton in dead region)

p

p

qjet

Z

ν_

ν

p

p

qjet

W

ν_

l

Monojets – Standard Model Backgrounds

p

p

qjet

g

jet

• Instrumentation + QCD– QCD dijets with one jet lost in dead region,

or due to energy fluctuations, or multijets– Calorimeter noise

– Beam induced signals– Cosmics

.

Monojets @ Tevatron and LHC

Tevatron Exclusion Limits

Number of Extra Dimensions2 3 4 5 6

Low

er L

imit

(TeV

)D

M

0.6

0.8

1

1.2

1.4

1.6 )-1

CDFII (1.1 fbD0 (RunI)LEP Combined

Number of Extra Dimensions2 3 4 5 6

Low

er L

imit

(TeV

)D

M

0.6

0.8

1

1.2

1.4

1.6

CDF II Preliminary

ATLAS

1

10

10 2

10 3

10 4

10 5

10 6

0 250 500 750 1000 1250 1500 1750 2000

jW(eν), jW(µν)

jW(τν)

jZ(νν)

total background

signal δ=2 MD = 4 TeV

signal δ=2 MD = 8 TeV

signal δ=3 MD = 5 TeV

signal δ=4 MD = 5 TeV

√s = 14 TeV

ETmiss (GeV)E

vent

s / 2

0 G

eV

Expected exclusion limits for 100 fb−1:

n 2 3 4

MD /TeV 9 7 6

Virtual Graviton Exchange in ADD

• e+e− and γγ from calorimeter measurements• µ+µ− momentum reconstruction in central and muon chambers

q

q_

G l-

l+ q

q_

G V

V

Look for deviations from SMin Drell-Yan scattering for e+e− and µ+µ−

q

q_

γ/Z l-

l+

Deviations expected at high invariant masses

as KK gravitons appear “massive”No deviations observed

Dimuon Mass (GeV)100 200 300 400 500 600 700 800

Eve

nts

/ 24

GeV

-210

-110

1

10

210

310

410

DataSM Background

)-4 = 1.0 TeVG

ηSM+ED signal ()-4 = 3.0 TeV

GηSM+ED signal (

-1DØ Run II, 246 pb

Virtual Graviton Exchange in ADD @ LHC

Bounds MD > 5− 10 TeVdepending on luminosity are expected at LHC

Significance vs. Luminosity

3000 4000 5000 6000 700010-3

10-2

10-1

100

101

102

103

Sig

nific

ance

(b)

n=6

5σσσσ

1000 fb -1

300 fb -1

100 fb -1

10 fb -1

1 fb -1

0.1 fb -1

MS, GeV

CMS reach for LED in µ+µ− channel

0.1 1 10 100 10002.53.03.54.04.55.05.56.06.57.07.58.08.59.09.5

10.010.5

100 fb-1

1 fb-1

ADD Discovery Limit

n = 6

n = 3

MS r

each

, TeV

Integrated Luminosity, fb-1

Quick discovery is possible with 1st data Belotelov et al.: CMS NOTE 2006-076

Large Extra Dimensions at LEP

Studied by all LEP experiments (ALEPH, DELPHI, OPAL, L3)

�� Real graviton productione+e− → γG , ZG

e+

e- V

G

�� Virtual graviton exchangee+e− → l+l− , qq̄ , VV

e+e- G l

-

l+ e+e- G V

V

Number of Extra Dimensions2 3 4 5 6

Low

er L

imit

(TeV

)D

M

0.6

0.8

1

1.2

1.4

1.6 )-1

CDFII (1.1 fbD0 (RunI)LEP Combined

Number of Extra Dimensions2 3 4 5 6

Low

er L

imit

(TeV

)D

M

0.6

0.8

1

1.2

1.4

1.6

CDF II Preliminary

http://cdsweb.cern.ch/record/962045

Black Holes

• Black Holes are predicted in general relativity theory (1915)

• Karl Schwarzschild solution (1916) for static non-spinning massive object –metric with singularity at Schwarzschild radius

RS =2MBHG

c2∝

1MPl

MBHMPl

If the radius of the object is < RS, black hole with event horizon at RS is formed

• The term “black hole” was introduced only around 1967 by John Wheeler

• Generalisation by Myers and Perry (1986) for D = 4+ n dimensions

RS ∝1

MD

(

MBHMD

)1

n+1

For small MD: RS is large

Black Hole Formation @ Hadron Colliders

• Big energies⇐⇒ small distances.

BH forms if partons come closer than 2RS

• BH mass M2BH = ŝ= (p1 + p2)2= x1x2s

Continuous mass spectrum starting at some M & MD

• Exact cross section needs quantum gravity theory.

Use quasi-classical “black disc” approximation:

σ̂ = fπR2 with formation factor f ∼ 1

Valid for MBH ≫ MD

• Possible for any combination of quarks and gluons.

All gauge and spin quantum numbers are allowed

• Large MBH ⇐⇒ large Bjorken x1, x2Quark-quark scattering dominates.BH are charged and coloured (B , 0)

qq

RS

RS – Schwarzschild radius

Black Hole Production @ LHC

• Cross section σ ≈ fπR2S ∝ M2BH = ŝ – Non-perturbative process

parton-parton σ grows with energy

——➤

. Of course, it decreases if folded with PDFs

• Hard perturbative processes are suppressedEvent horizon forms before particles have causal contact

“The end of short distance physics”

Black Hole Factory

Cross section σ ∼ πR2S ∼ 1 TeV−2 ∼ 10−38 m2 ∼ 100 pb

Rate may be very high, e.g. for MD = 1 TeV, MBH > 5 TeV, n = 10: rate ∼ 1 HzLHC would be “black hole factory”

1

10

10 2

10 3

10 4

10 5

10 6

10 7

10 8

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

MBH, GeV

dN/d

MB

H ×

500

GeV

MP = 1 TeV

MP = 3 TeV

MP = 5 TeV

MP = 7 TeV

——

➤

——

➤

n = 7 n = 2

background

Spectrum of BH at LHC decaying into final states with electron or photon

Hawking Radiation

• Steven Hawking showed (1975) that black hole can evaporate by emitting pairs of virtualphotons at event horizon, with one of photon escaping the BH gravity

• Photons have perfect black body spectrum with temperature

TH =~c

4πkBRS=

14πRS

∝ MPlMPlMBH

• No chance to discover Hawking radiation of astro black holes:sun mass TH ∼ nK ≪ TCMB = 2.7 K ; moon mass TH ∼ TCMB

• In D = 4+ n dimensions (Myers, Perry, 1986)

TH =n+ 14πRS

∝ MD

(

MDMBH

)1

n+1

(n+ 1)

• At high enough TH massive particles can also be produced

• In MC simulations at the LHC, Hawking radiation is approximated by democrating decay.

.

Black Hole Event Simulation @ ATLAS

–– High multiplicity

–– High sphericity

Democratic decay

q, g 72%

e, µ, τ 11%

W±,Z 8%

ν, G 6%

H 2%

γ 1%

h/l activity 5 : 1

h/γ activity 100 : 1

Approximation is valid only for MBH ≫ MD.

For MBH ∼ MD quantum gravity is needed.

Black Hole Event Selection

• To reduce QCD background from dijets/multijets, tt̄, cut∑

|pT | > 2.5 TeV

Various BH samples BH and backgrounds

Sum |Pt| / GeV0 1000 2000 3000 4000 5000 6000 7000 8000

Eve

nts

0

500

1000

1500

2000

2500

3000

3500

4000 n=2n=4

n=7

m>8TeV(x10)

ATLAS

Sum |Pt| / GeV0 1000 2000 3000 4000 5000 6000 7000 8000

Eve

nts

210

310

410

510

610

710 BH n=2J5J6J7J8ttbar

ATLAS

• Require at least one well identified lepton e or µ with pT > 50 GeV

QCD background further reduced by factor ∼ 60

Black Hole Discovery Potential

Robust estimation of discovery potential is difficult,because semi-classical model assumptions are valid only for MBH ≫ MD.Introduce artificial mass cut-off in generated samples =⇒ conservative estimation

BH Mass Threshold [TeV]5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

-1

Lu

min

osity

/ fb

-410

-310

-210

-110

1

10

210

310

ATLASn=2n=4n=7

Democratic Particle Distribution

Identify BH events ATLAS

Democratic decay in 120 SM degrees of freedom

emitted particle ratio reconstructed generator

electrons/muons 1653±1491701±173 = (97.2± 13.2)%16101661 = 96.9%

electrons/tops 1653±1496241±1631 = (26.5± 7.3)%16106234 = 25.8%

Z0/tops 1808±4646241±1631 = (29.0± 10.6)%18066234 = 29.0%

W±/tops 3112±9776241±1631 = (49.9± 20.4)%31186234 = 50.0%

Z0/W± 1808±4643112±977 = (58.1± 23.6)%18063118 = 57.9%

• A significant part of the democratic particle distribution could be reconstructed

• If there are black hole events, we will be able to identify them

Further Alternatives

• Little Higgs

• Compositeness

• Leptoquarks

LQq

e

• Unparticles, hidden world, . . .

More information in the next lecture course + journal club:Advanced Topics in Particle Physics (WS 2008)